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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol 1, 2011 Modeling of Flexural Waves in a Homogeneous Isotropic Rotating Cylindrical Panel P. Ponnusamy 1R .Selvamani 2* 1 Department of mathematics, Govt Arts College (Autonomous),Coimbatore, TamilNadu, India. 2 Department of mathematics, Karunya University,Coimbatore, TamilNadu, India. * E-mail of corresponding author:Selvam1729@gmail.com.AbstractThe flexural wave propagation in a homogeneous Isotropic rotating cylindrical panel is investigated inthe context of the linear theory of elasticity. Three displacement potential functions are introduced touncouple the equations of motion. The frequency equations are obtained using the traction free boundaryconditions. A modified Bessel functions with complex argument is directly used to analyze the frequencyequations and are studied numerically for the material copper. The computed Relative frequency shift isstudied for flexural(symmetric and skew-symmetric) modes and are plotted in the form of dispersion curveswith the support of MATLAB.Keywords: Isotropic cylindrical panel, Rotation,modified Bessel function.1.Introduction Since the speed of the disturbed waves depend upon rotation rate, this type of study is important inthe design of high speed steam , gas turbine and rotation rate sensors. The effect of rotation on cylindricalpanels has its applications in the diverse engineering field like civil, architecture, aeronautical and marineengineering. In the field of nondestructive evaluation, laser-generated waves have attracted greatattention owing to their potential application to noncontact and nondestructive evaluation of sheetmaterials. This study may be used in applications involving nondestructive testing (NDT), qualitativenondestructive evaluation (QNDE) of large diameter pipes and health monitoring of other ailinginfrastructures in addition to check and verify the validity of FEM and BEM for such problems.The theory of elastic vibrations and waves is well established [1]. An excellent collection of works onvibration of shells were published by Leissa [2]. Mirsky [3] analyzed the wave propagation in transverselyisotropic circular cylinder of infinite length and presented the numerical results. Gazis [4] has studied themost general form of harmonic waves in a hollow cylinder of infinite length. Ponnusamy [5] haveobtained the frequency equation of free vibration of a generalized thermo elastic solid cylinder of arbitrarycross section by using Fourier expansion collocation method. Sinha et. al. [6] have discussed theaxisymmetric wave propagation in circular cylindrical shell immersed in fluid in two parts. In Part I,thetheoretical analysis of the propagating modes are discussed and in Part II, the axisymmetric modes15 | P a g ewww.iiste.org

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Advances in Physics Theories and Applications www.iiste.orgISSN 2224-719X (Paper) ISSN 2225-0638 (Online)Vol 1, 2011excluding torsional modes are obtained theoretically and experimentally and are compared. Vibration offunctionally graded multilayered orthotropic cylindrical panel under thermo mechanical load was analyzedby Wang et.al [7]. Three dimensional vibration of a homogenous transversely isotropic thermo elasticcylindrical panel was investigated by Sharma [8]. Free vibration of transversely isotropic piezoelectriccircular cylindrical panels were studied by Ding et.al [9]. An iterative approach predict the frequency ofisotropic cylindrical shell and panel was studied by Soldatos and Hadhgeorgian [10]. Free vibration ofcomposite cylindrical panels with random material properties was developed by Sing et.al [11], in thiswork the effect of variations in the mechanical properties of laminated composite cylindrical panels on itsnatural frequency has been obtained by modeling these as random variables. Zhang [12] employed a wavepropagation method to analysis the frequency of cylindrical panels. Lam and Loy [13] investigated thevibration of thin cylindrical panels of simply supported boundary conditions with Flugge’s theory andalso studied the vibration of rotating cylindrical panel.The theory of elastic material with rotation isplays a vital role in civil, architecture, aeronautical and marine engineering . Body wave propagation inrotating thermo elastic media was investigated by Sharma and Grover [14]. The effect of rotation ,magnetofield, thermal relaxation time and pressure on the wave propagation in a generalized visco elastic mediumunder the influence of time harmonic source is discussed by Abd-Alla and Bayones[15].The propagation ofwaves in conducting piezoelectric solid is studied for the case when the entire medium rotates with auniform angula velocity by Wauer[16]. Roychoudhuri and Mukhopadhyay studied the effect of rotationand relaxation times on plane waves in generalized thermo visco elasticity[17].Gamer [18]discussed theelastic-plastic deformation of the rotating solid disk. Lam [19] studied the frequency characteristics of athin rotating cylindrical shell using general differential quadrature methodIn this paper, the three dimensional flexural wave propagation in a homogeneous isotropic rotatingcylindrical panel is discussed using the linear three-dimensional theory of elasticity. The frequencyequations are obtained using the traction free boundary conditions. A modified Bessel functions withcomplex argument is directly used to analyze the frequency by fixing the circumferential wave number andare studied numerically for the material copper. The computed Relative frequency shift5 is plotted in theform of dispersion curves .2. The Governing equationsConsider a cylindrical panel as shown in Fig.1 of length L having inner and outer radius a and b withthickness h. The angle subtended by the cylindrical panel, which is known as center angle, is denoted by . The deformation of the cylindrical panel in the direction r , , z are defined by u, v and w . Thecylindrical panel is assumed to be homogenous, isotropic and linearly elastic with a rotational speed ,Young’s modulus E, poisson ratio  and density  in an undisturbed state.16 | P a g ewww.iiste.org